Biosensor membranes composed of polymers containing heterocyclic nitrogens

ABSTRACT

Novel membranes comprising various polymers containing heterocyclic nitrogen groups are described. These membranes are usefully employed in electrochemical sensors, such as amperometric biosensors. More particularly, these membranes effectively regulate a flux of analyte to a measurement electrode in an electrochemical sensor, thereby improving the functioning of the electrochemical sensor over a significant range of analyte concentrations. Electrochemical sensors equipped wish such membranes are also described.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is claims priority to U.S. Provisional Application Ser.No. 60/291,215 of Fei Mao, filed on May 15, 2001 and entitled “BiosensorMembranes Composed of Polyvinylpyridines”, which is incorporated hereinin its entirety by this reference.

FIELD OF THE INVENTION

This invention generally relates to an analyte-flux-limiting membrane.More particularly, the invention relates to such a membrane composed ofpolymers containing heterocyclic nitrogens. The membrane is a usefulcomponent in biosensors, and more particularly, in biosensors that canbe implanted in a living body.

BACKGROUND OF THE INVENTION

Enzyme-based biosensors are devices in which ananalyte-concentration-dependent biochemical reaction signal is convertedinto a measurable physical signal, such as an optical or electricalsignal. Such biosensors are widely used in the detection of analytes inclinical, environmental, agricultural and biotechnological applications.Analytes that can be measured in clinical assays of fluids of the humanbody include, for example, glucose, lactate, cholesterol, bilirubin andamino acids. The detection of analytes in biological fluids, such asblood, is important in the diagnosis and the monitoring of manydiseases.

Biosensors that detect analytes via electrical signals, such as current(amperometric biosensors) or charge (coulometric biosensors), are ofspecial interest because electron transfer is involved in thebiochemical reactions of many important bioanalytes. For example, thereaction of glucose with glucose oxidase involves electron transfer fromglucose to the enzyme to produce gluconolactone and reduced enzyme. Inan example of an amperometric glucose biosensor, glucose is oxidized byoxygen in the body fluid via a glucose oxidase-catalyzed reaction thatgenerates gluconolactone and hydrogen peroxide, whereupon the hydrogenperoxide is electrooxidized and correlated to the concentration ofglucose in the body fluid. (Thome-Duret, V., et al., Anal. Chem. 68,3822 (1996); and U.S. Pat. No. 5,882,494 of Van Antwerp.) In anotherexample of an amperometric glucose biosensor, the electrooxidation ofglucose to gluconolactone is mediated by a polymeric redox mediator thatelectrically “wires” the reaction center of the enzyme to an electrode.(Csoregi, E., et al., Anal. Chem. 66, 3131 (1994); Csoregi, E., et al.,Anal. Chem. 67, 1240 (1995); Schmidtke, D. W., et al., Anal. Chem. 68,2845 (1996); Schmidtke, D. W., et al., Anal. Chem. 70, 2149 (1998); andSchmidtke, D. W., et al., Proc. Natl. Acad. Sci. U.S.A. 95, 294 (1998).)

Amperometric biosensors typically employ two or three electrodes,including at least one measuring or working electrode and one referenceelectrode. In two-electrode systems, the reference electrode also servesas a counter-electrode. In three-electrode systems, the third electrodeis a counter-electrode. The measuring or working electrode is composedof a non-corroding carbon or a metal conductor and is connected to thereference electrode via a circuit, such as a potentiostat.

Some biosensors are designed for implantation in a living animal body,such as a mammalian or a human body, merely by way of example. In animplantable amperometric biosensor, the working electrode is typicallyconstructed of a sensing layer, which is in direct contact with theconductive material of the electrode, and a diffusion-limiting membranelayer on top of the sensing layer. The sensing layer typically consistsof an enzyme, an enzyme stabilizer such as bovine serum albumin (BSA),and a crosslinker that crosslinks the sensing layer components.Alternatively, the sensing layer consists of an enzyme, a polymericmediator, and a crosslinker that crosslinks the sensing layercomponents, as in the above-mentioned “wired-enzyme” biosensor.

In an implantable amperometric glucose sensor, the membrane is oftenbeneficial or necessary for regulating or limiting the flux of glucoseto the sensing layer. By way of explanation, in a glucose sensor withouta membrane, the flux of glucose to the sensing layer increases linearlywith the concentration of glucose. When all of the glucose arriving atthe sensing layer is consumed, the measured output signal is linearlyproportional to the flux of glucose and thus to the concentration ofglucose. However, when the glucose consumption is limited by thekinetics of chemical or electrochemical activities in the sensing layer,the measured output signal is no longer controlled by the flux ofglucose and is no longer linearly proportional to the flux orconcentration of glucose. In this case, only a fraction of the glucosearriving at the sensing layer is consumed before the sensor becomessaturated, whereupon the measured signal stops increasing, or increasesonly slightly, with the concentration of glucose. In a glucose sensorequipped with a diffusion-limiting membrane, on the other hand, themembrane reduces the flux of glucose to the sensing layer such that thesensor does not become saturated and can therefor operate effectivelywithin a much wider range of glucose concentration.

More particularly, in these membrane-equipped glucose sensors, theglucose consumption rate is controlled by the diffusion or flux ofglucose through the membrane rather than by the kinetics of the sensinglayer. The flux of glucose through the membrane is defined by thepermeability of the membrane to glucose, which is usually constant, andby the concentration of glucose in the solution or biofluid beingmonitored. When all of the glucose arriving at the sensing layer isconsumed, the flux of glucose through the membrane to the sensing layervaries linearly with the concentration of glucose in the solution, anddetermines the measured conversion rate or signal output such that it isalso linearly proportional to the concentration of glucose concentrationin the solution. Although not necessary, a linear relationship betweenthe output signal and the concentration of glucose in the solution isideal for the calibration of an implantable sensor.

Implantable amperometric glucose sensors based on the electrooxidationof hydrogen peroxide, as described above, require excess oxygen reactantto ensure that the sensor output is only controlled by the concentrationof glucose in the body fluid or tissue being monitored. That is, thesensor is designed to be unaffected by the oxygen typically present inbody fluid or tissue. In body tissue in which the glucose sensor istypically implanted, the concentration of oxygen can be very low, suchas from about 0.02 mM to about 0.2 mM, while the concentration ofglucose can be as high as about 30 mM or more. Without aglucose-diffusion-limiting membrane, the sensor would become saturatedvery quickly at very low glucose concentrations. The sensor thusbenefits from having a sufficiently oxygen-permeable membrane thatrestricts glucose flux to the sensing layer, such that the so-called“oxygen-deficiency problem,” a condition in which there is insufficientoxygen for adequate sensing to take place, is minimized or eliminated.

In implantable amperometric glucose sensors that employ wired-enzymeelectrodes, as described above, there is no oxygen-deficiency problembecause oxygen is not a necessary reactant. Nonetheless, these sensorsrequire glucose-diffusion-limiting membranes because typically, forglucose sensors that lack such membranes, the current output reaches amaximum level around or below a glucose concentration of 10 mM, which iswell below 30 mM, the high end of clinically relevant glucoseconcentration.

A diffusion-limiting membrane is also of benefit in a biosensor thatemploys a wired-enzyme electrode, as the membrane significantly reduceschemical and biochemical reactivity in the sensing layer and thusreduces the production of radical species that can damage the enzyme.The diffusion-limiting membrane may also act as a mechanical protectorthat prevents the sensor components from leaching out of the sensorlayer and reduces motion-associated noise.

There have been various attempts to develop a glucose-diffusion-limitingmembrane that is mechanically strong, biocompatible, and easilymanufactured. For example, a laminated microporous membrane withmechanical holes has been described (U.S. Pat. No. 4,759,828 of Young etal.) and membranes formed from polyurethane are also known (Shaw, G. W.,et al., Biosensors and Bioelectronics 6, 401 (1991); Bindra, D. S., etal., Anal. Chem. 63, 1692 (1991); Shichiri, M., et al., Horm. Metab.Res., Suppl. Ser. 20, 17 (1988)). Supposedly, glucose diffuses throughthe mechanical holes or cracks in these various membranes. Further byway of example, a heterogeneous membrane with discrete hydrophobic andhydrophilic regions (U.S. Pat. No. 4,484,987 of Gough) and homogenousmembranes with both hydrophobic and hydrophilic functionalities (U.S.Pat. Nos. 5,284,140 and 5,322,063 of Allen et al.) have been described.However, all of these known membranes are difficult to manufacture andhave inadequate physical properties.

An improved membrane formed from a complex mixture of a diisocyanate, adiol, a diamine and a silicone polymer has been described in U.S. Pat.No. 5,777,060 (Van Antwerp), U.S. Pat. No. 5,786,439 (Van Antwerp etal.) and U.S. Pat. No. 5,882,494 (Van Antwerp). As described therein,the membrane material is simultaneously polymerized and crosslinked in aflask; the resulting polymeric material is dissolved in a strong organicsolvent, such as tetrahydroforan (THF); and the resulting solution isapplied onto the sensing layer to form the membrane. Unfortunately, avery strong organic solvent, such as THF, can denature the enzyme in thesensing layer and also dissolve conductive ink materials as well as anyplastic materials that may be part of the sensor. Further, since thepolymerization and crosslinking reactions are completed in the reactionflask, no further bond-making reactions occur when the solution isapplied to the sensing layer to form the membrane. As a result, theadhesion between the membrane layer and sensing layer may not beadequate.

In the published Patent Cooperation Treaty (PCT) Application bearingInternational Publication No. WO 01/57241 A2, Kelly and Schifferdescribe a method for making a glucose-diffusion-limiting membrane byphotolytically polymerizing small hydrophilic monomers. Thesensitivities of the glucose sensors employing such membranes are widelyscattered, however, indicating a lack of control in the membrane-makingprocess. Further, as the polymerization involves very small molecules,it is quite possible that small, soluble molecules remain afterpolymerization, which may leach out of the sensor. Thus, glucose sensorsemploying such glucose-diffusion-limiting membranes may not be suitablefor implantation in a living body.

SUMMARY OF THE INVENTION

The present invention is directed to membranes composed of crosslinkedpolymers containing heterocyclic nitrogen groups, particularly polymersof polyvinylpyridine and polyvinylimidazole, and to electrochemicalsensors equipped with such membranes. The membranes are useful inlimiting the flux of an analyte to a working electrode in anelectrochemical sensor so that the sensor is linearly responsive over alarge range of analyte concentrations and is easily calibrated.Electrochemical sensors equipped with membranes of the present inventiondemonstrate considerable sensitivity and stability, and a largesignal-to-noise ratio, in a variety of conditions.

According to one aspect of the invention, the membrane is formed bycrosslinking in situ a polymer, modified with a zwitterionic moiety, anon-pyridine copolymer component, and optionally another moiety that iseither hydrophilic or hydrophobic, and/or has other desirableproperties, in an alcohol-buffer solution. The modified polymer is madefrom a precursor polymer containing heterocyclic nitrogen groups.Preferably, the precursor polymer is polyvinylpyridine orpolyvinylimidazole. When used in an electrochemical sensor, the membranelimits the flux of an analyte reaching a sensing layer of the sensor,such as an enzyme-containing sensing layer of a “wired enzyme”electrode, and further protects the sensing layer. These qualities ofthe membrane significantly extend the linear detection range and thestability of the sensor.

In the membrane formation process, the non-pyridine copolymer componentgenerally enhances the solubility of the polymer and may provide furtherdesirable physical or chemical properties to the polymer or theresulting membrane. Optionally, hydrophilic or hydrophobic modifiers maybe used to “fine-tune” the permeability of the resulting membrane to ananalyte of interest. Optional hydrophilic modifiers, such aspoly(ethylene glycol), hydroxyl or polyhydroxyl modifiers, may be usedto enhance the biocompatibility of the polymer or the resultingmembrane. In the formation of a membrane of the present invention, thezwitterionic moiety of the polymer is believed to provide an additionallayer of crosslinking, via intermolecular electrostatic bonds, beyondthe basic crosslinking generally attributed to covalent bonds, and isthus believed to strengthen the membrane.

Another aspect of the invention concerns the preparation of asubstantially homogeneous, analyte-diffusion-limiting membrane that maybe used in a biosensor, such as an implantable amperometric biosensor.The membrane is formed in situ by applying an alcohol-buffer solution ofa crosslinker and a modified polymer over an enzyme-containing sensinglayer and allowing the solution to cure for one to two days. Thecrosslinker-polymer solution may be applied to the sensing layer byplacing a droplet or droplets of the solution on the sensor, by dippingthe sensor into the solution, or the like. Generally, the thickness ofthe membrane is controlled by the concentration of the solution, by thenumber of droplets of the solution applied, by the number of times thesensor is dipped in the solution, or by any combination of the thesefactors. Amperometric glucose sensors equipped with diffusion-limitingmembranes of the present invention demonstrate excellent stability andfast and linear responsivity to glucose concentration over a largeglucose concentration range.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of a typical structure of a section of ananalyte-diffusion-limiting membrane, according to the present invention.

FIG. 2A is a schematic, side-view illustration of a portion of atwo-electrode glucose sensor having a working electrode, a combinedcounter/reference electrode, and a dip-coated membrane that encapsulatesboth electrodes, according to the present invention. FIGS. 2B and 2C areschematic top- and bottom-view illustrations, respectively, of theportion of the glucose sensor of FIG. 2A. Herein, FIGS. 2A, 2B and 2Cmay be collectively referred to as FIG. 2.

FIG. 3 is a graph of current versus glucose concentration for sensorshaving glucose-diffusion-limiting membranes, according to the presentinvention, and for sensors lacking such membranes, based on averagevalues.

FIG. 4 is a graph of current output versus time at fixed glucoseconcentration for a sensor having a glucose-diffusion-limiting membrane,according to the present invention, and for a sensor lacking such amembrane.

FIG. 5 is a graph of current output versus time at different levels ofglucose concentration for sensors having glucose-diffusion-limitingmembranes, according to the present invention, based on average values.

FIG. 6 is a graph of current output versus time at different levels ofglucose concentration, with and without stirring, for a sensor having aglucose-diffusion-limiting membrane, according to the present invention,and for a sensor lacking such a membrane.

FIG. 7A is a graph of current output versus glucose concentration forfour separately prepared batches of sensors havingglucose-diffusion-limiting membranes, according to the presentinvention, based on average values. FIGS. 7B-7E are graphs of currentoutput versus glucose concentration for individual sensors in each ofthe four above-referenced batches of sensors havingglucose-diffusion-limiting membranes, respectively, according to thepresent invention. Herein, FIGS. 7A, 7B, 7C, 7D and 7E may becollectively referred to as FIG. 7.

DESCRIPTION OF THE INVENTION

When used herein, the terms in quotation marks are defined as set forthbelow.

The term “alkyl” includes linear or branched, saturated aliphatichydrocarbons. Examples of alkyl groups include methyl, ethyl, n-propyl,isopropyl, n-butyl, tert-butyl and the like. Unless otherwise noted, theterm “alkyl” includes both alkyl and cycloalkyl groups.

The term “alkoxy” describes an alkyl group joined to the remainder ofthe structure by an oxygen atom. Examples of alkoxy groups includemethoxy, ethoxy, n-propoxy, isopropoxy, butoxy, tert-butoxy, and thelike. In addition, unless otherwise noted, the term ‘alkoxy’ includesboth alkoxy and cycloalkoxy groups.

The term “alkenyl” describes an unsaturated, linear or branchedaliphatic hydrocarbon having at least one carbon-carbon double bond.Examples of alkenyl groups include ethenyl, 1-propenyl, 2-propenyl,1-butenyl, 2-methyl-1-propenyl, and the like.

A “reactive group” is a functional group of a molecule that is capableof reacting with another compound to couple at least a portion of thatother compound to the molecule. Reactive groups include carboxy,activated ester, sulfonyl halide, sulfonate ester, isocyanate,isothiocyanate, epoxide, aziridine, halide, aldehyde, ketone, amine,acrylamide, thiol, acyl azide, acyl halide, hydrazine, hydroxylamine,alkyl halide, imidazole, pyridine, phenol, alkyl sulfonate,halotriazine, imido ester, maleimide, hydrazide, hydroxy, andphoto-reactive azido aryl groups. Activated esters, as understood in theart, generally include esters of succinimidyl, benzotriazolyl, or arylsubstituted by electron-withdrawing groups such as sulfo, nitro, cyano,or halo groups; or carboxylic acids activated by carbodiimides.

A “substituted” functional group (e.g., substituted alkyl, alkenyl, oralkoxy group) includes at least one substituent selected from thefollowing: halogen, alkoxy, mercapto, aryl, alkoxycarbonyl,alkylaminocarbonyl, dialkylaminocarbonyl, —OH, —NH2, alkylamino,dialkylamino, trialkylammonium, alkanoylamino, arylcarboxamido,hydrazino, alkylthio, alkenyl, and reactive groups.

A “crosslinker” is a molecule that contains at least two reactive groupscapable of linking at least two molecules together, or linking at leasttwo portions of the same molecule together. Linking of at least twomolecules is called intermolecular crosslinking, while linking of atleast two portions of the same molecule is called intramolecularcrosslinking. A crosslinker having more than two reactive groups may becapable of both intermolecular and intramolecular crosslinkings at thesame time.

The term “precursor polymer” refers to the starting polymer before thevarious modifier groups are attached to form a modified polymer.

The term “heterocyclic nitrogen group” refers to a cyclic structurecontaining a sp² hybridized nitrogen in a ring of the structure.

The term “polyvinylpyridine” refers to poly(4-vinylpyridine),poly(3-vinylpyridine), or poly(2-vinylpyridine), as well as anycopolymer of vinylpyridine and a second or a third copolymer component.

The term “polyvinylimidazole” refers to poly(1-vinylimidazole),poly(2-vinylimidazole), or poly(4-vinylimidazole).

A “membrane solution” is a solution that contains all necessarycomponents for crosslinking and forming the membrane, including amodified polymer containing heterocyclic nitrogen groups, a crosslinkerand a buffer or an alcohol-buffer mixed solvent.

A “biological fluid” or “biofluid” is any body fluid or body fluidderivative in which the analyte can be measured, for example, blood,interstitial fluid, plasma, dermal fluid, sweat, and tears.

An “electrochemical sensor” is a device configured to detect thepresence of or measure the concentration or amount of an analyte in asample via electrochemical oxidation or reduction reactions. Typically,these reactions can be transduced to an electrical signal that can becorrelated to an amount or concentration of analyte.

A “redox mediator” is an electron-transfer agent for carrying electronsbetween an analyte, an analyte-reduced or analyte-oxidized enzyme, andan electrode, either directly, or via one or more additionalelectron-transfer agents. A redox mediator that includes a polymericbackbone may also be referred to as a “redox polymer”.

The term “reference electrode” includes both a) reference electrodes andb) reference electrodes that also function as counter electrodes (i.e.,counter/reference electrodes), unless otherwise indicated.

The term “counter electrode” includes both a) counter electrodes and b)counter electrodes that also function as reference electrodes (i.e.,counter/reference electrodes), unless otherwise indicated.

In general, membrane of the present invention is formed by crosslinkinga modified polymer containing heterocyclic nitrogen groups in analcohol-buffer mixed solvent and allowing the membrane solution to cureover time. The polymer comprises poly(heterocyclic nitrogen-containingconstituent) as a portion of its backbone and additional elements,including a zwitterionic moiety, a hydrophobic moiety, and optionally, abiocompatible moiety. The resulting membrane is capable of limiting theflux of an analyte from one space, such as a space associated with abiofluid, to another space, such as space associated with anenzyme-containing sensing layer. An amperometric glucose sensorconstructed of a wired-enzyme sensing layer and aglucose-diffusion-limiting layer of the present invention is very stableand has a large linear detection range.

Heterocyclic-Nitrogen Containing Polymers

The polymer of the present invention has the following general formula,Formula 1a:

wherein the horizontal line represents a polymer backbone; A is an alkylgroup substituted with a water soluble group, preferably a negativelycharged group, such as sulfonate, phosphate, or carboxylate, and morepreferably, a strong acid group such as sulfonate, so that thequaternized heterocyclic nitrogen to which it is attached iszwitterionic; D is a copolymer component of the polymer, as furtherdescribed below; each of n, l, and p is independently an average numberof an associated polymer unit or polymer units shown in the closestparentheses to the left; and q is a number of a polymer unit or polymerunits shown in the brackets.

The heterocyclic nitrogen groups of Formula 1 a include, but are notlimited to, pyridine, imidazole, oxazole, thiazole, pyrazole, or anyderivative thereof. Preferably, the heterocyclic nitrogen groups areindependently vinylpyridine, such as 2-, 3-, or 4-vinylpyridine, orvinylimidazole, such as 1-, 2-, or 4-vinylimidazole. More preferably,the heterocyclic nitrogen groups are independently 4-vinylpyridine, suchthat the more preferable polymer is a derivative ofpoly(4-vinylpyridine). An example of such a poly(4-vinylpyridine) of thepresent invention has the following general formula, Formula 1b:

wherein A, D, n, l, p and q are as described above in relation toFormula 1a.

While the polymer of the present invention has the general Formula 1a orFormula 1b above, it should be noted that when A is a strong acid, suchas a stronger acid than carboxylic acid, the D component is optional,such that p may equal zero. Such a polymer of the present invention hasthe following general formula, Formula 1c:

wherein A is a strong acid and the heterocyclic nitrogen groups, n, land q are all as described above. Sulfonate and fluorinated carboxylicacid are examples of suitably strong acids. It is believed that when Ais a sufficiently strong acid, the heterocyclic nitrogen to which it isattached becomes zwitterionic and thus capable of forming intermolecularelectrostatic bonds with the crosslinker during membrane formation. Itis believed that these intermolecular electrostatic bonds provideanother level of crosslinking, beyond the covalent bonds typical ofcrosslinking, and thus make the resulting membrane stronger. As aresult, when A is a suitably strong acid, the D component, which isoften a strengthening component such as styrene, may be omitted from thepolymers of Formulas 1a and 1b above. When A is a weaker acid, such thatthe heterocyclic nitrogen is not zwitterionic or capable of formingintermolecular electrostatic bonds, the polymer of the present inventiondoes include D, as shown in Formulas 1a and 1b above.

Examples of A include, but are not limited to, sulfopropyl, sulfobutyl,carboxypropyl, and carboxypentyl. In one embodiment of the invention,group A has the formula -L-G, where L is a C2-C12 linear or branchedalkyl linker optionally and independently substituted with an aryl,alkoxy, alkenyl, alkynyl, —F, —Cl, —OH, aldehyde, ketone, ester, oramide group, and G is a negatively charged carboxy or sulfonate group.The alkyl portion of the substituents of L have 1-6 carbons and arepreferably an aryl, —OH or amide group.

A can be attached to the heterocyclic nitrogen group via quaternizationwith an alkylating agent that contains a suitable linker L and anegatively charged group G, or a precursor group that can be convertedto a negatively charged group G at a later stage. Examples of suitablealkylating agents include, but are not limited to,2-bromoethanesulfonate, propanesultone, butanesultone, bromoacetic acid,4-bromobutyric acid and 6-bromohexanoic acid. Examples of alkylatingagents containing a precursor group include, but are not limited to,ethyl bromoacetate and methyl 6-bromohexanoate. The ethyl and methylester groups of these precursors can be readily converted to anegatively charged carboxy group by standard hydrolysis.

Alternatively, A can be attached to the heterocyclic nitrogen group byquaternizing the nitrogen with an alkylating agent that contains anadditional reactive group, and subsequently coupling, via standardmethods, this additional reactive group to another molecule thatcontains a negatively charged group G and a reactive group. Typically,one of the reactive groups is an electrophile and the other reactivegroup is a nucleophile. Selected examples of reactive groups and thelinkages formed from their interactions are shown in Table 1. TABLE 1Examples of Reactive Groups and Resulting Linkages First Reactive GroupSecond Reactive Group Resulting Linkage Activated ester* Amine AmideAcrylamide Thiol Thioether Acyl azide Amine Amide Acyl halide AmineAmide Carboxylic acid Amine Amide Aldehyde or ketone Hydrazine HydrazoneAldehyde or ketone Hydroxyamine Oxime Alkyl halide Amine AlkylamineAlkyl halide Carboxylic acid Ester Alkyl halide Imidazole ImidazoliumAlkyl halide Pyridine Pyridinium Alkyl halide Alcohol/phenol Ether Alkylhalide Thiol Thioether Alkyl sulfonate Thiol Thioether Alkyl sulfonatePyridine Pyridinium Alkyl sulfonate Imidazole Imidazolium Alkylsulfonate Alcohol/phenol Ether Anhydride Alcohol/phenol Ester AnhydrideAmine Amide Aziridine Thiol Thioether Aziridine Amine AlkylamineAziridine Pyridine Pyridinium Epoxide Thiol Thioether Epoxide AmineAlkylamine Epoxide Pyridine Pyridinium Halotriazine Amine AminotriazineHalotriazine Alcohol Triazinyl ether Imido ester Amine AmidineIsocyanate Amine Urea Isocyanate Alcohol Urethane Isothiocyanate AmineThiourea Maleimide Thiol Thioether Sulfonyl halide Amine Sulfonamide*Activated esters, as understood in the art, generally include esters ofsuccinimidyl, benzotriazolyl, or aryl substituted byelectron-withdrawing groups such as sulfo, nitro, cyano, or halo; orcarboxylic acids activated by carbodiimides.By way of example, A may be attached to the heterocyclic nitrogen groupsof the polymer by quaternizing the heterocyclic nitrogens with6-bromohexanoic acid and subsequently coupling the carboxy group to theamine group of 3-amino-1-propanesulfonic acid in the presence of acarbodiimide coupling agent.

D is a component of a poly(heterocyclic nitrogen-co-D) polymer ofFormula 1a or 1b. Examples of D include, but are not limited to,phenylalkyl, alkoxystyrene, hydroxyalkyl, alkoxyalkyl,alkoxycarbonylalkyl, and a molecule containing a poly(ethylene glycol)or polyhydroxyl group. Some poly(heterocyclic nitrogen-co-D)polymerssuitable as starting materials for the present invention arecommercially available. For example, poly(2-vinylpyridine-co-styrene),poly(4-vinylpyridine-co-styrene) and poly(4-vinylpyridine-co-butylmethacrylate) are available from Aldrich Chemical Company, Inc. Otherpoly(heterocyclic nitrogen-co-D)polymers can be readily synthesized byanyone skilled in the art of polymer chemistry using well-known methods.Preferably, D is a styrene or a C1-C18 alkyl methacrylate component of apolyvinylpyridine-poly-D, such as (4-vinylpyrine-co-styrene) orpoly(4-vinylpyridine-co-butyl methacrylate), more preferably, theformer. D may contribute to various desirable properties of the membraneincluding, but not limited to, hydrophobicity, hydrophilicity,solubility, biocompatibility, elasticity and strength. D may be selectedto optimize or “fine-tune” a membrane made from the polymer in terms ofits permeability to an analyte and its non-permeability to anundesirable, interfering component, for example.

The letters n, l, and p designate, respectively, an average number ofeach copolymer component in each polymer unit. The letter q is one for ablock copolymer or a number greater than one for a copolymer with anumber of repeating polymer units. By way of example, the q value for apolymer of the present invention may be ≧about 950, where n, l and p are1, 8 and 1, respectively. The letter q is thus related to the overallmolecular weight of the polymer. Preferably, the average molecularweight of the polymer is above about 50,000, more preferably above about200,000, most preferably above about 1,000,000.

The polymer of the present invention may comprise a further, optionalcopolymer, as shown in the following general formula, Formula 2a:

wherein the polymer backbone, A, D, n, l, p and q are as described abovein relation to Formulas 1a-1c; m is an average number of an associatedpolymer unit or polymer units shown in the closest parentheses to theleft; and B is a modifier. When the heterocyclic nitrogen groups are4-substituted pyridine, as is preferred, the polymer of the presentinvention is derivative of poly(4-vinylpyridine) and has the generalformula, Formula 2b, set forth below.

Further, when A is a suitably strong acid, as described above, the Dcopolymer is optional, in which case the polymer of the presentinvention has the general formula, Formula 2c:

In any of Formulas 2a-2c, B is a modifier group that may add any desiredchemical, physical or biological properties to the membrane. Suchdesired properties include analyte selectivity, hydrophobicity,hydrophilicity, elasticity, and biocompatibility. Examples of modifiersinclude the following: negatively charged molecules that may minimizeentrance of negatively charged, interfering chemicals into the membrane;hydrophobic hydrocarbon molecules that may increase adhesion between themembrane and sensor substrate material; hydrophilic hydroxyl orpolyhydroxy molecules that may help hydrate and add biocompatibility tothe membrane; silicon polymers that may add elasticity and otherproperties to the membrane; and poly(ethylene glycol) constituents thatare known to increase biocompatibility of biomaterials (Bergstrom, K.,et al., J. Biomed. Mat. Res. 26, 779 (1992)). Further examples of Binclude, but are not limited to, a metal chelator, such as a calciumchelator, and other biocompatible materials. A poly(ethylene glycol)suitable for biocompatibility modification of the membrane generally hasa molecular weight of from about 100 to about 20,000, preferably, fromabout 500 to about 10,000, and more preferably, from about 1,000 toabout 8,000.

The modifier B can be attached to the heterocyclic nitrogens of thepolymer directly or indirectly. In direct attachment, the heterocyclicnitrogen groups may be reacted with a modifier containing an alkylatinggroup. Suitable alkylating groups include, but are not limited to, alkylhalide, epoxide, aziridine, and sulfonate esters. In indirectattachment, the heterocyclic nigrogens of the polymer may be quaternizedwith an alkylating agent having an additional reactive group, and thenattached to a molecule having a desired property and a suitable reactivegroup.

As described above, the B-containing copolymer is optional in themembrane of the present invention, such that when m of Formula 2a-2c iszero, the membrane has the general formula of Formula 1a-1c,respectively. The relative amounts of the four copolymer components, theheterocyclic nitrogen group containing A, the optional heterocyclicnitrogen group containing B, the heterocyclic nitrogen group, and D, maybe expressed as percentages, as follows: [n/(n+m+l+p)]×100%,[m/(n+m+l+p)]×100%, [l/(n+m+l+p)]×100%, and [p/(n+m+l+p)]×100%,respectively. Suitable percentages are 1-25%, 0-15% (when theB-containing heterocyclic nitrogen group is optional) or 1-15%, 20-90%,and 0-50% (when D is optional) or 1-50%, respectively, and preferablepercentages are 5-20%, 0-10% (when the B-containing heterocyclicnitrogen group is optional) or 1-10%, 60-90%, and 5-20%, respectively.

Specific examples of suitable polymers have the general formulas,Formulas 3-6, shown below.

EXAMPLES OF SYNTHESES OF POLYVINYLPYRIDINE POLYMERS

Examples showing the syntheses of various polyvinylpyridine polymersaccording to the present invention are provided below. Numerical figuresprovided are approximate.

Example 1 Synthesis of a Polymer of Formula 3

By way of illustration, an example of the synthesis of a polymer ofFormula 3 above, is now provided. A solution ofpoly(4-vinylpyridine-co-styrene) (˜10% styrene content) (20g, Aldrich)in 100 mL of dimethyl formamide (DMF) at 90° C. was stirred and6-bromohexanoic acid (3.7 g) in 15-20 mL of DMF was added. The resultingsolution was stirred at 90° C. for 24 hours and then poured into 1.5 Lof ether, whereupon the solvent was decanted. The remaining, gummy solidwas dissolved in MeOH (150-200 mL) and suction-filtered through amedium-pore, fritted funnel to remove any undissolved solid. Thefiltrate was added slowly to rapidly stirred ether (1.5 L) in a beaker.The resulting precipitate was collected by suction filtration and driedat 50° C. under high vacuum for 2 days. The polymer had the followingparameters: [n/(n+l+p)]×100%≈10%; [l/(n+l+p)]×100%≈80%; and[p/(n+l+p)]×100%≈10%.

Example 2 Synthesis of a Polymer of Formula 5

By way of illustration, an example of the synthesis of a polymer ofFormula 5 above, is now provided. A solution ofpoly(4-vinylpyridine-co-styrene) (˜10% styrene) (20 g, Aldrich) in 100mL of anhydrous DMF at 90° C. was stirred, methanesulfonic acid (˜80mg)was added, and then 2 g of methoxy-PEG-epoxide (molecular weight 5,000)(Shearwater Polymers, Inc.) in 15-20 mL of anhydrous DMF was added. Thesolution was stirred at 90° C. for 24 hours and 1,3-Propane sultone(2.32 g) in 10 mL of anhydrous DMF was added. The resulting solution wascontinuously stirred at 90° for 24 hours, and then cooled to roomtemperature and poured into 800 mL of ether. The solvent was decantedand the remaining precipitate was dissolved in hot MeOH (˜200 mL),suction-filtered, precipitated again from 1 L of ether, and then driedat 50° C. under high vacuum for 48 hours. The resulting polymer has thefollowing parameters: [n/(n+m+l+p)]×100%≈10%; [m/(n+m+l+p)]×100%≈10%;[l/(n+m+l+p)]×100%≈70%; [p/(n+m+l+p)]×100%≈10%.

Example 3 Synthesis of a Polymer Having a Polyhydroxy Modifier B

By way of illustration, an example of the synthesis of a polymer havinga polyhydroxy modifier B, as schematically illustrated below, is nowprovided. Various polyhydroxy compounds are known for havingbiocompatibility properties. (U.S. Pat. No. 6,011,077.) The synthesisbelow illustrates how a modifier group having a desired property may beattached to the polymer backbone via a linker.

1,3-propane sultone (0.58 g, 4.8 mmoles) and 6-bromohexanoic acid (1.85g, 9.5 mmoles) are added to a solution ofpoly(4-vinylpyridine-co-styrene) (˜10% styrene) (10 g) dissolved in 60mL of anhydrous DMF. The resulting solution is stirred at 90° C. for 24hours and then cooled to room temperature.O—(N-succinimidyl)-N,N,N′,N′-tetramethyl-uronium tetrafluoroborate(TSTU) (2.86 g, 9.5 mmoles) and N,N-diisopropylethylamine (1.65 mL, 9.5mmoles) are then added in succession to the solution. After the solutionis stirred for 5 hours, N-methyl-D-glucamine (2.4 g, 12.4 mmoles) isadded and the resulting solution is stirred at room temperature for 24hours. The solution is poured into 500 ml of ether and the precipitateis collected by suction filtration. The collected precipitate is thendissolved in MeOH/H₂O and the resulting solution is subjected to ultramembrane filtration using the same MeOH/H₂O solvent to remove smallmolecules. The dialyzed solution is evaporated to dryness to give apolymer with the following parameters: [n/(n+m+l+p)]×100%≈10%;[m/(n+m+l+p)]×100%≈10%; [l/(n+m+l+p)]×100%≈70%; and[p/(n+m+l+p)]×100%≈10%.Crosslinkers

Crosslinkers of the present invention are molecules having at least tworeactive groups, such as bi-, tri-, or tetra-functional groups, capableof reacting with the heterocyclic nitrogen groups, pyridine groups, orother reactive groups contained on A, B or D of the polymer. Preferably,the reactive groups of the crosslinkers are slow-reacting alkylatinggroups that can quaternize the heterocyclic nitrogen groups, such aspyridine groups, of the polymer. Suitable alkylating groups include, butare not limited to, derivatives of poly(ethylene glycol) orpoly(propylene glycol), epoxide (glycidyl group), aziridine, alkylhalide, and sulfonate esters. Alkylating groups of the crosslinkers arepreferably glycidyl groups. Preferably, glycidyl crosslinkers have amolecular weight of from about 200 to about 2,000 and are water solubleor soluble in a water-miscible solvent, such as an alcohol. Examples ofsuitable crosslinkers include, but are not limited to, poly(ethyleneglycol)diglycidyl ether with a molecular weight of about 200 to about600, and N,N-diglycidyl-4-glycidyloxyaniline.

It is desirable to have a slow crosslinking reaction during thedispensing of membrane solution so that the membrane coating solutionhas a reasonable pot-life for large-scale manufacture. A fastcrosslinking reaction results in a coating solution of rapidly changingviscosity, which renders coating difficult. Ideally, the crosslinkingreaction is slow during the dispensing of the membrane solution, andaccelerated during the curing of the membrane at ambient temperature, orat an elevated temperature where possible.

Membrane Formation and Sensor Fabrication

An example of a process for producing a membrane of the presentinvention is now described. In this example, the polymer of the presentinvention and a suitable crosslinker are dissolved in abuffer-containing solvent, typically a buffer-alcohol mixed solvent, toproduce a membrane solution. Preferably, the buffer has a pH of about7.5 to about 9.5 and the alcohol is ethanol. More preferably, the bufferis a 10 mM (2-(4-(2-hydroxyethyl)-1-piperazine)ethanesulfonate) (HEPES)buffer (pH 8) and the ethanol to buffer volume ratio is from about 95 to5 to about 0 to 100. A minimum amount of buffer is necessary for thecrosslinking chemistry, especially if an epoxide or aziridinecrosslinker is used. The amount of solvent needed to dissolve thepolymer and the crosslinker may vary depending on the nature of thepolymer and the crosslinker. For example, a higher percentage of alcoholmay be required to dissolve a relatively hydrophobic polymer and/orcrosslinker.

The ratio of polymer to cross-linker is important to the nature of thefinal membrane. By way of example, if an inadequate amount ofcrosslinker or an extremely large excess of crosslinker is used,crosslinking is insufficient and the membrane is weak. Further, if amore than adequate amount of crosslinker is used, the membrane is overlycrosslinked such that membrane is too brittle and/or impedes analytediffusion. Thus, there is an optimal ratio of a given polymer to a givencrosslinker that should be used to prepare a desirable or usefulmembrane. By way of example, the optimal polymer to crosslinker ratio byweight is typically from about 4:1 to about 32:1 for a polymer of any ofFormulas 3-6 above and a poly(ethylene glycol)diglycidyl ethercrosslinker, having a molecular weight of about 200 to about 400. Mostpreferably, this range is from about 8:1 to about 16:1. Further by wayof example, the optimal polymer to crosslinker ratio by weight istypically about 16:1 for a polymer of Formula 4 above, wherein[n/(n+l+p)]×100%≈10%, [l(n+l+p)]×100%≈80%, and [p/(n+l+p)]×100%≈10%, orfor a polymer of Formula 5 above, wherein [n/(n+m+l+p)]×100%≈10%,[m/(n+m+l+p)]×100%≈10%, [l/(n+m+l+p)]×100%≈70%, [p/(n+m+l+p)]×100%≈10%,and and a poly(ethylene glycol)diglycidyl ether crosslinker having amolecular weight of about 200.

The membrane solution can be coated over a variety of biosensors thatmay benefit from having a membrane disposed over the enzyme-containingsensing layer. Examples of such biosensors include, but are not limitedto, glucose sensors and lactate sensors. (See U.S. Pat. No. 6,134,461 toHeller et al., which is incorporated herein in its entirety by thisreference.) The coating process may comprise any commonly usedtechnique, such as spin-coating, dip-coating, or dispensing droplets ofthe membrane solution over the sensing layers, and the like, followed bycuring under ambient conditions typically for 1 to 2 days. Theparticular details of the coating process (such as dip duration, dipfrequency, number of dips, or the like) may vary depending on the nature(i.e., viscosity, concentration, composition, or the like) of thepolymer, the crosslinker, the membrane solution, the solvent, and thebuffer, for example. Conventional equipment may be used for the coatingprocess, such as a DSG D1L-160 dip-coating or casting system of NIMATechnology in the United Kingdom.

Example of Sensor Fabrication

Sensor fabrication typically consists of depositing an enzyme-containingsensing layer over a working electrode and casting thediffusion-limiting membrane layer over the sensing layer, andoptionally, but preferably, also over the counter and referenceelectrodes. The procedure below concerns the fabrication of atwo-electrode sensor, such as that depicted in FIGS. 2A-2C. Sensorshaving other configurations such as a three-electrode design can beprepared using similar methods.

A particular example of sensor fabrication, wherein the numericalfigures are approximate, is now provided. A sensing layer solution wasprepared from a 7.5 mM HEPES solution (0.5 μL, pH 8), containing 1.7 μgof the polymeric osmium mediator compound L, as disclosed in PublishedPatent Cooperation Treaty (PCT) Application, International PublicationNo. WO 01/36660 A2, which is incorporated herein in its entirety by thisreference; 2.1 μg of glucose oxidase (Toyobo); and 1.3 μg ofpoly(ethylene glycol)diglycidyl ether (molecular weight 400). Compound Lis shown below.

The sensing layer solution was deposited over carbon-ink workingelectrodes and cured at room temperature for two days to produce anumber of sensors. A membrane solution was prepared by mixing 4 volumesof a polymer of Formula 4 above, dissolved at 64 mg/mL in 80% EtOH/20%HEPES buffer (10 mM, pH 8), and one volume of poly(ethyleneglycol)diglycidyl ether (molecular weight 200), dissolved at 4 mg/mL in80% EtOH/20% HEPES buffer (10 mM, pH 8). The above-described sensorswere dipped three times into the membrane solution, at about 5 secondsper dipping, with about a 10-minute time interval between consecutivedippings. The sensors were then cured at room temperature and normalhumidity for 24 hours.

An approximate chemical structure of a section of a typical membraneprepared according to the present invention is shown in FIG. 1. Such amembrane may be employed in a variety of sensors, such as the two- orthree-electrode sensors described previously herein. By way of example,the membrane may be used in a two-electrode amperometric glucose sensor,as shown in FIG. 2A-2C (collectively FIG. 2) and described below.

The amperometric glucose sensor 10 of FIG. 2 comprises a substrate 12disposed between a working electrode 14 that is typically carbon-based,and a Ag/AgCl counter/reference electrode 16. A sensor or sensing layer18 is disposed on the working electrode. A membrane or membrane layer 20encapsulates the entire glucose sensor 10, including the Ag/AgClcounter/reference electrode.

The sensing layer 18 of the glucose sensor 10 consists of crosslinkedglucose oxidase and a low potential polymeric osmium complex mediator,as disclosed in the above-mentioned Published PCT Application,International Publication No. WO 01/36660 A2. The enzyme- andmediator-containing formulation that can be used in the sensing layer,and methods for applying them to an electrode system, are known in theart, for example, from U.S. Pat. No. 6,134,461. According to the presentinvention, the membrane overcoat was formed by thrice dipping the sensorinto a membrane solution comprising 4 mg/mL poly(ethyleneglycol)diglycidyl ether (molecular weight of about 200) and 64 mg/mL ofa polymer of Formula 4 above, wherein [n/(n+l+p)]×100%≈10%;[l/(n+l+p)]×100%≈80%; and [p/(n+l+p)]×100%≈10%, and curing thethrice-dipped sensor at ambient temperature and normal humidity for atleast 24 hours, such as for about 1 to 2 days. The q value for such amembrane overcoat may be≈about 950, where n, l and p are 1, 8 and 1,respectively.

Membrane Surface Modification

Polymers of the present invention have a large number of heterocyclicnitrogen groups, such as pyridine groups, only a few percent of whichare used in crosslinking during membrane formation. The membrane thushas an excess of these groups present both within the membrane matrixand on the membrane surface. Optionally, the membrane can be furthermodified by placing another layer of material over theheterocyclic-nitrogen-group-rich or pyridine-rich membrane surface. Forexample, the membrane surface may be modified by adding a layer ofpoly(ethylene glycol) for enhanced biocompatibility. In general,modification may consist of coating the membrane surface with amodifying solution, such as a solution comprising desired moleculeshaving an alkylating reactive group, and then washing the coatingsolution with a suitable solvent to remove excess molecules. Thismodification should result in a monolayer of desired molecules.

The membrane 20 of the glucose sensor 10 shown in FIG. 2 may be modifiedin the manner described above.

Experimental Examples

Examples of experiments that demonstrate the properties and/or theefficacy of sensors having diffusion-limiting membranes according to thepresent invention are provided below. Numerical figures provided areapproximate.

Calibration Experiment

In a first example, a calibration experiment was conducted in whichfifteen sensors lacking membranes were tested simultaneously (Set 1),and separately, eight sensors having diffusion-limiting membranesaccording to the present invention were tested simultaneously (Set 2),all at 37° C. In Set 2, the membranes were prepared from polymers ofFormula 4 above and poly(ethylene glycol)diglycidyl ether (PEGDGE)crosslinkers, having a molecular weight of about 200. In the calibrationexperiment for each of Set 1 and Set 2, the sensors were placed in aPBS-buffered solution (pH 7) and the output current of each of thesensors was measured as the glucose concentration was increased. Themeasured output currents (μA for Set 1; nA for Set 2) were then averagedfor each of Set 1 and Set 2 and plotted against glucose concentration(mM), as shown in the calibration graph of FIG. 3.

As shown, the calibration curve for the Set 1 sensors lacking membranesis approximately linear over a very small range of glucoseconcentrations, from zero to about 3 mM, or 5 mM at most. This resultindicates that the membrane-free sensors are insufficiently sensitive toglucose concentration change at elevated glucose concentrations such as10 mM, which is well below the high end of clinically relevant glucoseconcentration at about 30 mM. By contrast, the calibration curve for theSet 2 sensors having diffusion-limiting membranes according to thepresent invention is substantially linear over a relatively large rangeof glucose concentrations, for example, from zero to about 30 mM, asdemonstrated by the best-fit line (y=1.2502x+1.1951; R²≈0.997) alsoshown in FIG. 3. This result demonstrates the considerable sensitivityof the membrane-equipped membranes to glucose concentration, at low,medium, and high glucose concentrations, and of particular relevance, atthe high end of clinically relevant glucose concentration at about 30mM.

Stability Experiment

In a second example, a stability experiment was conducted in which asensor lacking a membrane and a sensor having a diffusion-limitingmembrane according to the present invention were tested, simultaneously,at 37° C. The membrane-equipped sensor had a membrane prepared from thesame polymer and the same crosslinker as those of the sensors of Set 2described above in the calibration experiment. In this stabilityexperiment, each of the sensors was placed in a PBS-buffered solution(pH 7) having a fixed glucose concentration of 30 mM, and the outputcurrent of each of the sensors was measured. The measured outputcurrents (μA for the membrane-less sensor; nA for the membrane-equippedsensor) were plotted against time (hour), as shown in the stabilitygraph of FIG. 4.

As shown, the stability curve for the membrane-less sensor decaysrapidly over time, at a decay rate of about 4.69% μA per hour. Thisresult indicates a lack of stability in the membrane-less sensor. Bycontrast, the stability curve for the membrane-equipped sensor accordingto the present invention shows relative constancy over time, or noappreciable decay over time, the decay rate being only about 0.06% nAper hour. This result demonstrates the considerable stability andreliability of the membrane-equipped sensors of the present invention.That is, at a glucose concentration of 30 mM, while the membrane-lesssensor lost sensitivity at a rate of almost 5% per hour over a period ofabout 20 hours, the membrane-equipped sensor according to the presentinvention showed virtually no loss of sensitivity over the same period.

Responsivity Experiment

Ideally, the membrane of an electrochemical sensor should not impedecommunication between the sensing layer of the sensor and fluid orbiofluid containing the analyte of interest. That is, the membraneshould respond rapidly to changes in analyte concentration.

In a third example, a responsivity experiment was conducted in whicheight sensors having diffusion-limiting membranes according to thepresent invention were tested simultaneously (Set 3), all at 37° C. Thesensors of Set 3 had membranes prepared from the same polymers and thesame crosslinkers as those of the sensors of Set 2 described in thecalibration experiment above. In this responsivity experiment, the eightsensors were placed in a PBS-buffered solution (pH 7), the glucoseconcentration of which was increased in a step-wise manner over time, asillustrated by the glucose concentrations shown in FIG. 5, and theoutput current of each of the sensors was measured. The measured outputcurrents (nA) were then averaged for Set 3 and plotted against time(real time, hour:minute:second), as shown in the responsivity graph ofFIG. 5.

The responsivity curve for the Set 3 sensors having diffusion-limitingmembranes according to the present invention has discrete steps thatmimic the step-wise increases in glucose concentration in a rapidfashion. As shown, the output current jumps rapidly from one plateau tothe next after the glucose concentration is increased. This resultdemonstrates the considerable responsivity of the membrane-equippedsensors of the present invention. The responsivity of thesemembrane-equipped electrochemical sensors makes them ideal for analytesensing, such as glucose sensing.

Motion-Sensitivity Experiment

Ideally, the membrane of an electrochemical sensor should be unaffectedby motion or movement of fluid or biofluid containing the analyte ofinterest. This is particularly important for a sensor that is implantedin a body, such as a human body, as body movement may causemotion-associated noise and may well be quite frequent.

In this fourth example, a motion-sensitivity experiment was conducted inwhich a sensor A lacking a membrane was tested, and separately, a sensorB having a diffusion-limiting membrane according to the presentinvention was tested, all at 37° C. Sensor B had a membrane preparedfrom the same polymer and the same crosslinker as those of the sensorsof Set 2 described in the calibration experiment above. In thisexperiment, for each of test, the sensor was placed in a beakercontaining a PBS-buffered solution (pH 7) and a magnetic stirrer. Theglucose concentration of the solution was increased in a step-wisemanner over time, in much the same manner as described in theresponsivity experiment above, as indicated by the various mM labels inFIG. 6. The stirrer was activated during each step-wise increase in theglucose concentration and deactivated some time thereafter, asillustrated by the “stir on” and “stir off” labels shown in FIG. 6. Thisactivation and deactivation of the stirrer was repeated in a cyclicalmanner at several levels of glucose concentration and the output currentof each of the sensors was measured throughout the experiment. Themeasured output currents (pA for sensor A; nA for sensor B) were plottedagainst time (minute), as shown in the motion-sensitivity graph of FIG.6.

As shown, the output current for the membrane-less sensor A is greatlyaffected by the stir versus no stir conditions over the glucoseconcentration range used in the experiment. By contrast, the outputcurrent for sensor B, having diffusion-limiting membranes according tothe present invention, is virtually unaffected by the stir versus nostir conditions up to a glucose concentration of about 10 mM, and onlyslightly affected by these conditions at a glucose concentration ofabout 15 mM. This result demonstrates the considerable stability of themembrane-equipped sensors of the present invention in both stirred andnon-stirred environments. The stability of these membrane-equippedelectrochemical sensors in an environment of fluid movement makes themideal for analyte sensing within a moving body.

Sensor Reproducibility Experiment

Dip-coating, or casting, of membranes is typically carried out usingdipping machines, such as a DSG D1L-160 of NIMA Technology of the UnitedKingdom. Reproducible casting of membranes has been considered quitedifficult to achieve. (Chen, T., et al., In Situ AssembledMass-Transport Controlling Micromembranes and Their Application inImplanted Amperometric Glucose Sensors, Anal. Chem., Vol. 72, No. 16,Pp. 3757-3763 (2000).) Surprisingly, sensors of the present inventioncan be made quite reproducibly, as demonstrated in the experiment nowdescribed.

Four batches of sensors (Batches 1-4) were prepared separately accordingto the present invention, by dipping the sensors in membrane solutionthree times using casting equipment and allowing them to cure. In eachof the four batches, the membrane solutions were prepared from thepolymer of Formula 4 and poly(ethylene glycol)digycidyl ether (PEDGE)crosslinker having a molecular weight of about 200 (as in Set 2 andother Sets described above) using the same procedure. The membranesolutions for Batches 1 and 2 were prepared separately from each other,and from the membrane solution used for Batches 3 and 4. The membranesolution for Batches 3 and 4 was the same, although the Batch 3 andBatch 4 sensors were dip-coated at different times using differentcasting equipment. That is, Batches 1, 2 and 3 were dip-coated using anon-commercial, built system and Batch 4 was dip-coated using theabove-referenced DSG D1L-160 system.

Calibration tests were conducted on each batch of sensors at 37° C. Foreach batch, the sensors were placed in PBS-buffered solution (pH 7) andthe output current (nA) of each of the sensors was measured as theglucose concentration (mM) was increased. For each sensor in each of thefour batches, a calibration curve based on a plot of the current outputversus glucose concentration was prepared as shown in FIG. 7B (Batch 1:5 sensors), FIG. 7C (Batch 2: 8 sensors), FIG. 7D (Batch 3: 4 sensors)and FIG. 7E (Batch 4: 4 sensors). The average slopes of the calibrationcurves for each batch were the following:

-   -   Batch 1: Average Slope=1.10 nA/mM (CV=5%);    -   Batch 2: Average Slope=1.27 nA/mM (CV=10%);    -   Batch 3: Average Slope=1.15 nA/mM (CV=5%); and    -   Batch 4: Average Slope=1.14 nA/mM (CV=7%).        Further, for each batch, the current output for the sensors in        the batch was averaged and plotted against glucose        concentration, as shown in FIG. 7A. The average slope for        Batches 1-4 was 1.17 nA/mM (CV=7.2%).

The slopes of the curves within each batch and from batch-to-batch arevery tightly grouped, showing considerably little variation. The resultsdemonstrate that sensors prepared according to the present inventiongive quite reproducible results, both within a batch and frombatch-to-batch.

The foregoing examples demonstrate many of the advantages of themembranes of the present invention and the sensors employing suchmembranes. Particular advantages of sensors employing the membranes ofthe present invention include sensitivity, stability, responsivity,motion-compatibility, ease of calibration, and ease and reproducibilityof manufacture.

Various aspects and features of the present invention have beenexplained or described in relation to beliefs or theories, although itwill be understood that the invention is not bound to any particularbelief or theory. Various modifications, processes, as well as numerousstructures to which the present invention may be applicable will bereadily apparent to those of skill in the art to which the presentinvention is directed upon review of the specification. Although thevarious aspects and features of the present invention have beendescribed with respect to various embodiments and specific examplesherein, it will be understood that the invention is entitled toprotection within the full scope of the appended claims.

1-89. (canceled)
 90. A crosslinked membrane for use in an analyticalsensor, comprising: a polymer having the formula:

wherein the solid horizontal line represents a polymer backbone; A is analkyl substituted with a water-soluble constituent; D is selected fromphenylalkyl, alkoxystyrene, hydroxyalkyl, alkoxyalkyl,alkoxycarbonylalkyl, a poly(ethylene glycol)-containing constituent, anda polyhydroxyl-containing constituent; and each of n, l, p and q isindependently a positive number.
 91. The membrane of claim 90, wherein Ais negatively charged.
 92. The membrane of claim 90, wherein A isselected from a sulfonate, a carboxylate, and a phosphate.
 93. Themembrane of claim 90, wherein A is selected from sulfopropyl,sulfobutyl, carboxypropyl, and carboxypentyl.
 94. The membrane of claim90, wherein A is of the formula L-G, where L is a C2-C12 linear orbranched alkyl linker and G is a negatively charged carboxy orsulfonate.
 95. The membrane of claim 94, wherein L is substituted withan aryl, alkoxy, alkenyl, alkynyl, —F, —Cl, —OH, aldehyde, ketone,ester, or amide.
 96. The membrane of claim 90, wherein D is styrene orC1-C18 alkyl methacrylate.
 97. The membrane of claim 90, wherein anaverage molecular weight of the polymer is above about 50,000.
 98. Themembrane of claim 90, wherein an average molecular weight of the polymeris above about 50,000 to about 200,000.
 99. The membrane of claim 90,wherein the polymer further comprises a B-containing copolymer such thatthe polymer has the formula:

wherein B is a modifier and m is a positive number.
 100. The membrane ofclaim 99, wherein B is selected from a chelator, a negatively chargedconstituent, a hydrophobic hydrocarbon constituent, a hydrophilichydroxyl or polyhydroxy constituent, a silicon polymer, and apoly(ethylene glycol).
 101. The membrane of claim 99, wherein B is apoly(ethylene glycol) having a molecular weight of from about 100 toabout 20,000.
 102. The membrane of claim 99, wherein B is apoly(ethylene glycol) having a molecular weight of from about 200 toabout
 2000. 103. The membrane of claim 99, wherein [n/(n+m+l+p)]×100% isfrom about 1% to about 25%.
 104. The membrane of claim 99, wherein[m/(n+m+l+p)]×100% is from about 1% to about 15%.
 105. The membrane ofclaim 99, wherein [l/(n+m+l+p)]×100% is from about 20% to about 90%.106. The membrane of claim 99, wherein [p/(n+m+l+p)]×100% is from about1% to about 50%.
 107. The membrane of claim 90, wherein at least oneheterocyclic nitrogen constituent of the polymer is independentlyselected from pyridine, imidazole, oxazole, thiazole, pyrazole, and anyderivative thereof.
 108. The membrane of claim 90 sufficient to limit aflux of glucose or lactate thereacross.
 109. The membrane of claim 90sufficient to limit a flux of glucose or lactate thereacross in vivo.110. An electrochemical sensor, comprising: a working electrodecomprising: a sensing layer in contact with a conductive material of theelectrode; a membrane disposed over the sensing layer, the membranecomprising a polymer having the formula:

wherein the solid horizontal line represents a polymer backbone; A is analkyl substituted with a water-soluble constituent; D is selected fromphenylalkyl, alkoxystyrene, hydroxyalkyl, alkoxyalkyl,alkoxycarbonylalkyl, a poly(ethylene glycol)-containing constituent, anda polyhydroxyl-containing constituent; and each of n, l, p and q isindependently a positive number; and a counter electrode inelectrochemical communication with the working electrode.